Generalized Matrix rings are ubiquitous in algebra and have relevant applications to analysis. A ring is quasi-Baer ( right p.q.-Baer) in case the right annihilator of any ideal (resp. principal ideal) is generated by an idempotent. A ring is called biregular if every principal right ideal is generated by a central idempotent. A ring is called right FI-extending ( right strongly FI-extending) if every fully invariant submodule is essential in a direct summand (resp. fully invariant direct summand). In this paper we identify the ideals and principal ideals, the annihilators of ideals and the central, semi-central and general idempotents of a 2 × 2 matrix ring. We characterize the generalized matrix rings that are quasi-Baer, p.q.-Baer and biregular and we present structural features of right FI-extending and right strongly FI-extending rings. We provide examples to illustrate these concepts.
|Advisor:||Birkenmeier, Gary F.|
|Commitee:||Heatherly, Henry E., Lynd, Justin, Magidin, Arturo|
|School:||University of Louisiana at Lafayette|
|School Location:||United States -- Louisiana|
|Source:||DAI-B 80/08(E), Dissertation Abstracts International|
|Keywords:||Biregular, FI-extending, Generalized matrix rings, Idempotents, Quasi-Baer, p.q. Baer|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be